The invention is in the field of systems and methods for processing patterns, such as oriented patterns, to derive constituents which are more useful than the original patterns, and to deform the patterns into more useful forms. For example, in accordance with the invention an oriented pattern such as a seismic section can be decomposed into a flow field, which can be thought of as an estimate of a moving accretion boundary which formed the subsurface layers, and a residual pattern, which can be thought of as defining layer properties, such as acoustic velocity. The flow field can then be used to deform the pattern such that the parameter of interest in the pattern can be viewed and/or further processed more conveniently. For example, the seismic section can be deformed such that all of the subsurface horizons are along one regular (e.g., orthogonal) coordinate, and can thus all be horizontal. This can immensely simplify further processing because, for example, the many seismic horizons in a typical section need not be traced along their respective typically wavy lines to find subsurface features of interest, such as faults and discontinuities, but along the straight lines of one of the coordinates of the pattern deformed in accordance with the invention.
Machine perception of patterns is a problem common to many fields, and a need has long existed to transform patterns in a way which emphasizes or extracts features which are particularly useful in some overall process. One relatively simple example is in camera auto-focusing, where the useful feature of the image pattern on the focusing screen is its degree of sharpness as the focusing ring turns, as opposed to features such as what objects are in the frame, or what is the overall exposure. As another relatively simple example, an intrinsic property such as the shape of a workpiece can be the feature of interest where it is desirable to have a robot arm recognize as equivalent all workpieces which are similarly shaped, regardless of how they differ in other pattern features, such as color, texture, illumination, etc. While these examples typify a class of problems in machine perception of images, the invention here has a different emphasis.
A common problem in computational vision is how to decompose a pattern into intrinsic patterns (e.g., depth, reflectance and illuminance) which can be more useful than image intensity in some overall process because they can describe more basic and more independent constituents of the pattern forming process. Thus, for example, if a computational vision system separates shape from illumination, it can recognize shape regardless of changing illumination. The advantages of decomposing a pattern into more-or-less independent constituents in order to enhance its usefulness in some process can extend to processes which make use of the way in which the object giving rise to the pattern originates. For example, a system which could decompose a pattern which corresponds to the image of a bent rod into two constituents, a straight rod and a bending transformation, can find the similarity between a bent rod and one which has not been bent, or some other solid bent the same way.
One class of patterns which can be of significant interest in fields such as exploration for subsurface resources, e.g., hydrocarbons and minerals, is oriented patterns, notably those produced by processes such as propagation, accretion, or deformation. An example of a pattern produced by propagation is that of the deposits left by the movement of a prehistoric glacier; an example for accretion is the pattern of the sediments at the bottom of a prehistoric body of water; and an example of deformation is the pattern of subsurface strata deformed by a tectonic movement. If such patterns can be effectively decomposed into a constituent indicative of what was propagating or accreting or deforming, and a constituent indicative of which way and how much, then the constituents can benefit an overall process of exploration for, and exploitation of, underground resources, or some other overall process, more than the original pattern. More precisely, the desired decomposition in accordance with the invention can be into an estimate everywhere of the direction and magnitude of the anisotropy of the pattern (or of the "flow field" of the pattern), and of the residual pattern which is significantly independent of the flow field. For example:
(a) a typical oriented pattern created by propagation is the streaked trail left by a paint brush; the flow field of that pattern can describe the trajectory of the brush, which can be useful in a process pertaining to trajectory control, and the residual pattern then depends on the distribution of paint on the brush, which can be useful in a process pertaining to supplying paint to the brush; PA1 (b) a typical pattern created by accretion is a laminar structure, such as wood grain; here the flow field can define isochrones (the moving accretion boundary) and the residual pattern can give the change in color or brightness of the accreting material over time; and PA1 (c) if an isotropic body is deformed, the flow field principally describes the bending and stretching it has undergone, while the residual pattern describes the undeformed body.
As another example, which can be of a more immediate interest in the use of this invention, a seismic section can be processed in accordance with the invention as an oriented pattern in which the flow field can define the subsurface horizons, and the residual pattern can define the change in acoustic velocity across the horizons. Yet another example can be the pattern derived from a borehole tool (well logging tool) which can measure subsurface resistivity as a function of both borehole depth and angle around the borehole wall, and can give an output in the form of a column charting resistivity changes with depth along the long, vertical dimension and with angle in the short, horizontal dimension. This output can be processed as an oriented pattern such that, for example, the subsurface layers which dip in nature are in fact displayed as horizontal bands, with appropriate correction for the relative positions of display points. The changes in properties with depth can then be simply traced along the vertical dimension, without having to account for dip in the tracing process. Similarly, changes with angle can be simply traced along straight horizontal lines.
In all these examples, separate descriptions of the flow field and the residual pattern can be useful because they describe different processes. The path of propagation of a physical process can be controlled by mechanisms very different from those controlling the nature of the material left behind. The mechanism which controls the shape of an accretion boundary can be different from that creating the layer material. The forces which deform a rod can be different from those which created the rod in the first place. If these properties of patterns can be separated, then the isolated and hence simplified features can be more meaningful or useful than without the separation.
While various proposals have been made concerning the machine perception of oriented patterns in various fields, it is believed that the complexity of the analysis has proved to be a substantial impediment to achieving useful results. Accordingly, one object of the invention pertains to processing oriented patterns in a particularly efficacious way to find the flow field. Another pertains to a significant departure from known prior proposals--the use, in accordance with the invention, of the flow field to define the residual pattern in a natural coordinate system derived from the flow field, and thus provide significant and unexpected benefits in processes making use of the flow field and/or the residual pattern. Yet another pertains to the processing of the residual pattern along one or more coordinates of the natural coordinate system derived from the flow field.
Stated differently, in accordance with the invention, an oriented pattern can be processed to find its flow field and if desired to define it in terms, for example, of a grid of flow lines and lines locally transverse to the flow lines. This grid, which typically is made up of wavy lines, can then be mapped into regular coordinates, for example orthogonal coordinates, to "straighten" the grid lines and thereby deform the pattern into a residual pattern, i.e., the constituent of the original pattern which is substantially independent of the flow field which caused the distribution of the parameter of interest in the original pattern. Because the grid lines are based on an estimate of the flow field, they can be considered as a more natural coordinate system than the one in which the pattern is originally represented, and the regular coordinates into which the grid lines are mapped to transform the original pattern into the deformed pattern (also called the residual pattern or constituent), they too can be considered as more natural for the parameter of interest.
In accordance with one example of the invention, an oriented pattern can be processed first to estimate its flow field, for example by finding local estimates of flow directions in the pattern and using them to find an estimate of the overall flow field. A flow field grid can be constructed on the basis of the estimated flow field, and can be considered as a natural coordinate system for the original oriented pattern. This grid of typically wavy lines can then be mapped into regular (e.g., orthogonal or polar) coordinates, which also can be viewed as natural coordinates for the parameter of interest. Transforming the original pattern into those regular "flow" (or natural) coordinates, can straighten the original pattern, removing the effects of changing orientation and making it a more useful residual (or deformed) pattern.
Specifically, in one exemplary and nonlimiting embodiment of the invention, a pattern after initial filtering is processed to measure the gradient of a parameter such as image intensity (or a subsurface property, such as resistivity) at each point (or elemental area or volume) in the pattern. The gradient angle is then doubled, to map directions differing by 180.degree. into a single direction, and the transformed gradient vectors are summed over a weighted neighborhood around the respective point in the pattern. The angle of the summed vector is halved, to undo the previous transformation. This gives an estimate for the direction of greatest variance in the parameter of interest, which is then rotated by 90.degree. to yield the local flow direction. In practice, this can be done by a machine-implemented process equivalent to convolving the pattern I(x,y) with an isotropic bandpass filter H(x,y) to produce a convolved pattern C(x,y) in which the filter is applied to each of a number of selected elements of the pattern. The convolved pattern C(x,y) is localled differentiated by finite differences to find the local change in a selected parameter of the pattern in the x-direction (C.sub.x) and in the y-direction (C.sub.y) at each of a number of selected locations (x,y) in the pattern. These can be used to derive local measures J.sub.1 (x,y)=2C.sub.x (x,y)C.sub.y (x,y) and J.sub.2 (x,y)=C.sub.x.sup.2 (x,y)-C.sub.y.sup.2 (x,y), which are in turn convolved with a local weighting function W(x,y) to derive respective local measures J.sub.1 *(x,y) and J.sub.2 *(x,y). The local angle phi of the direction of greatest change of a selected parameter of the pattern can then be derived in accordance with the relationship EQU .phi.(x,y).apprxeq.tan.sup.-1 (J.sub.1 *(x,y)/J.sub.2 *(x,y))/2
In addition to finding the local direction of anisotropy (the local estimate of flow direction) by such local estimates, it can be important to find how strong the anisotropy is at each point of interest in the pattern. If the gradient vectors around a particular point on the pattern are not very different, then the orientation of the slight anisotropy at that point may not be very significant. Conversely, if the gradient is much stronger in one direction, this can be quite meaningful. For this reason, a measure called local coherence can be found, in accordance with the invention, of how significant the distribution of gradient vectors is at each point (or at least each point of interest) in the pattern. If the gradient vectors are close to uniform around a pattern point, the local coherent measure would be close to zero; if the only gradient vector having a significant magnitude points in a given direction, then the coherence measure is close to one; in between, the coherence measure increases with the peak of gradient vectors getting narrower. In order to estimate the reliability of the local estimate of flow direction in accordance with a particular embodiment of the invention as a machine-implemented process, a local coherence X(x,y) can be found by finding a third local measure J.sub.3 (x,y)=[C.sub.x.sup.2 (x,y)+C.sub.y.sup.2 (x,y)].sup.1/2 and convolving it with the same local weighting function W(x,y) to derive a third local measure J.sub.3 *(x,y). The local coherence X(x,y) of the local flow directions can then be found in accordance with the relationship EQU X(x,y)=(J.sub.1 *(x,y).sup.2 +J.sub.2 *(x,y).sup.2).sup.1/2 /J.sub.3 *(x,y)
The estimates of local flow directions and of local flow coherence can, but need not, be displayed.
The flow field can be thought of as an abstraction of the anisotropy of the pattern, which may not be apparent from observing or otherwise processing the original pattern. For example, patterns composed of bands, irregular streaks, and dot pairs can have the same flow field. In addition to finding the flow field, it may be useful to find the underlying pattern constituent which is independent of the changing direction of anisotropy in the original pattern. Finding the underlying, residual pattern can reveal, for example, that two very different flow fields are defined by the same kinds of bands or streaks in the original pattern.
A powerful way to remove the effect of changing orientation of the anisotropy in the original pattern in accordance with the invention, is to literally straighten the pattern, by subjecting it to a transformation which maps the typically wavy flow field lines into regular coordinates, e.g., straight, parallel lines in a canonical, e.g., horizontal, orientation. In this example, this can be thought of as a process which starts with an original pattern which shows how a residual pattern looks after it is bent, and gives a transformed pattern which shows how the residual pattern looked before it was bent to form the original pattern. While for many overall processes it may not be necessary to explicitly represent or show the residual pattern in the regular coordinates into which the flow field grid can be mapped, the ability in accordance with the invention to estimate the flow field and use coordinates based on it can be highly useful in itself toward the goal of decomposing the original pattern into constituents which are simpler than the original pattern and are more closely tied to independent parts of the physical processes likely to have led to the creation of the original pattern.
In a particular example of practicing this aspect of the invention as a machine-implemented process, a location (e.g., element or area or pixel) of the original pattern is selected, and the desired grid lines are traced by taking steps of respective fixed arc-length along flow lines which are locally along the local flow directions and along transverse lines which are locally across the local flow directions. This typically gives a grid of wavy lines which are transverse, e.g., perpendicular, to each other where they intersect.
In order to "straighten" the pattern, i.e., deform it into a pattern which is represented in desired regular coordinates so as to bring out the residual pattern, free of the estimated influence of the flow field, the typically wavy grid lines are mapped onto a regular coordinate system. In the example of a regular coordinate system which is orthogonal, each typically wavy grid line becomes a straight line, and the pattern elements which were on the wavy line are now on a straight line. Bilinear interpolation can be used to interpolate the wavy grid lines from the nearby local estimates of flow direction, and to interpolate the values of elements (pixels) of the deformed pattern (the residual pattern) from nearby elements of the original pattern.
The regular coordinates are particularly useful for estimating changes in a selected parameter of the deformed pattern in a direction along or across the flow field, which is often of primary interest. While in the original pattern wavy lines have to be followed for this purpose, which can present difficulties in a machine-impleneted process for pattern processing, in a residual (deformed) pattern derived in accordance with the invention this is not the case, because in the case of using orthogonal regular coordinates, at each point the flow direction is a straight line and the direction across the flow also is a straight line. If the regular coordinate system into which the original pattern is transformed to derive the residual pattern is not orthogonal, then the directions with and across the flow are still regular, e.g., along an arc in the case of the theta coordinate in a polar (r, theta) coordinate system.
One relatively simple example of a benefit of the invention is in edge detection. In an original pattern in which the flow field is not apparent, it can be difficult to select a meaningful direction in which to look for edges and, additionally, it can be difficult to follow or maintain a meaningful direction which started out well. However, this is immensely simplified when, in accordance with the invention, a direction along or across the regularized flow field coordinates can be selected and easily followed. In the example of a seismic section, a machine process for detecting acoustic velocity transitions between subsurface layers can be immensely simplified and speeded up if the section can be represented in orthogonal flow field coordinates, because then the search can be in straight lines perpendicular to the layer boundaries in the new, regularized flow field coordinate system of the residual (deformed or transformed) pattern. The search for anomalies can be similarly enhanced. For example a simple search in straight lines along (or parallel to) the other coordinate in the new coordinate system (along the flow direction) can locate anomalies such as missing sections or faults in the subsurface formations. Geological models can be fitted to the pattern which has been "straightened" by using regularized flow field coordinates in accordance with the invention much more easily, and can be manipulated in that coordinate system much more easily than in the coordinate system of the original pattern, to thereby speed up the exploration of the subsurface formations for underground resources.
Another example of the invention is in characterizing subsurface structures in terms of depositional history. For example, a well logging tool designated by the mark MST, carries a number of transducers which measure subsurface resistivity along segments of a narrow fan which can have its apex at the tool and spread in a plane perpendicular to the long axis of the tool. The processed output of the tool can be similar in appearance to the image of a core sample in the logged subsurface formations. If the formations are dipping, the tool output would show a column of short lines (straight or wavy) which are at an angle to the horizontal corresponding to the dip angle in the relevant vertical plane. The short lines can be parallel to each other if the dip is constant, but at an angle to each other if the dip changes with depth in the borehole. If in accordance with the invention the tool output is deformed to a coordinate system in which both the dip lines and the subsurface layers (or beds) are all horizontal, then parameters such as resistivity per subsurface bed, changed in resistivity along a direction perpendicular to the direction in which the layers were deposited in the first place, and other parameters pertaining to the depositional history, or the tectonic movement history, of the subsurface layers, can be much more easily estimated and further processed by using the new coordinate system, and therefore can be much more useful in the exploration for, and exploitation of, underground resources. In different fields, the invention can be useful in processing other oriented patterns, such as interference patterns which can be decomposed into a flow field and a residual pattern in an effort to determine what caused the interference pattern. While the invention is described as applied to two-dimensional patterns, its principles apply to three-dimensional patterns as well, which can be thought of as made up of a stack of two-dimensional patterns. As yet another nonlimiting example of the invention, decomposing a pattern which has resulted from a deformation of an isotropic body into a flow field and a residual pattern in accordance with the invention, can allow finding a physical deformation which requires least energy, or finding other physical parameters useful in subsequent processes. Other aspects of the invention will become apparent from the detailed description below.